The Effect of Linear Time Trends on Cointegration Testing in Single Equations

Abstract

This paper surveys the asymptotic distributions of three widely used single equation cointegration tests. Particular attention is paid to the case where the regressors are integrated with drift, i.e. at least one of the regressors follows a linear trend. Even if the regressions are not detrended, the asymptotic critical values are affected by the presence of linear trends in the regressors. Not taking into account this effect leads to tests that are biased towards establishing cointegration too often. The correct limiting distribution theory of regressions without detrending in the presence of integrated regressors with drift is described. Appropriate critical values are readily available from the literature and are simple to use following the tables included here.